Dynamical Stability of Formation of Cortical Maps

A cortical map is a localized neural representation of the signals in the outer world. A rough map is formed under the guidance of genetic information at the initial stage of development, but it is modified and refined further by self-organization. The persent paper gives a mathematical theory of formation of a cortical map by self-organization. The theory treats both dynamic of excitation patterns and dynamics of self-organization in a neural field. This not only explains the resolution and amplification properties of a cortical map, but elucidates the dynamical stability of such a map. This explains the emergence of a microcolumnar or mosaic structure in the cerebrum.